Introduction to Methods for Nonlinear Optimization

Prof. Luigi Grippo was formerly a full professor of operations research at the University of Rome "La Sapienza" and he taught courses on operations research, optimization algorithms, approximation methods, mathematical programming, computer learning. His research work has been mainly concerned with methods for nonlinear optimization and computer learning. He has published more than 40 papers on international journals and has served as associate editor in the Journal Optimization Methods and Software.Prof. Marco Sciandrone is a full professor of Operations Research at University of Rome “La Sapienza”.  He teaches courses on operations research, continuous  optimization and machine learning. His research interests include nonlinear optimization and machine learning.  He has published about 60 papers on international journals. He is associate editor of the journals Optimization Methods and Software, and 4OR. He was one of the founders of DEIX srl, a start-up of University of Rome “La Sapienza”.

• 1 Introduction.-2 Fundamental definitions and basic existence results.- 3 Optimality conditions for unconstrained problems in Rn.- 4 Optimality conditions for problems with convex feasible set.- 5 Optimality conditions for Nonlinear Programming.- 6 Duality theory.- 7 Optimality conditions based on theorems of the alternative.- 8 Basic concepts on optimization algorithms.- 9 Unconstrained optimization algorithms.- 10 Line search methods.- 11 Gradient method.- 12 Conjugate direction methods.- 13 Newton’s method.- 14 Trust region methods.- 15 Quasi-Newton Methods.- 16 Methods for nonlinear equations.- 17 Methods for least squares problems.- 18 Methods for large-scale optimization.- 19 Derivative-free methods for unconstrained optimization.- 20 Methods for problems with convex feasible set.- 21 Penalty and augmented Lagrangian methods.- 22 SQP methods.- 23 Introduction to interior point methods.- 24 Nonmonotone methods.- 25 Spectral gradient methods.- 26 Decomposition methods.- Appendix A: basic concepts of linear algebra and analysis.- Appendix B: Differentiation in Rn.- Appendix C: Introduction to convex analysis.

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